Stack of woods
- Autor:
- Andreas Lindner
- Thema:
- Folgen und Reihen
The harmonic series
The series is named harmonic series.
It is divergent.
About the meaning of the divergence of the harmonic series
You can stack woods or books on top of each other so that they create a certain overhang.
What is the maximum overhang?
Task
Illustrate the problem in the applet provided.
Increse the number of woods.
Hint
For the calculation of the barycenter, see also the teaching material Der Schwerpunkt (in German).
Derivation of the center of gravity coordinates (in German)
Total overhang
For the total overhang for the nth wood, this results in the sum of all individual overhangs
.
Since the harmonic sum diverges, this means that you can create an overhang of any size with an appropriate number of woods.